Monthly Archives: January 2025

Test Your Intuition (58): Polyhedra with 5-sided and 6-sided faces.

Posted on January 29, 2025 by Gil Kalai

Let F be the class of planar 3-connected cubic graphs with n vertices, with all faces (including the outer face) are either pentagons or hexagons. Equivalently, F can be viewed as the family of graphs of simple 3-polytopes with n … Continue reading →

Posted in Combinatorics, Convex polytopes, Test your intuition | Tagged | 2 Comments

Annotated Pictures from Fall 2024

Posted on January 26, 2025 by Gil Kalai

Apart from pictures, I write about the very first “Test your Intuition” question, a pioneering work of Tutubalin, the hierarchy of valuations of Lehman, Lehman, and Nisan, and three conjectures of Miki Tarsi. September 2024 Rothschild Symposium From left to … Continue reading →

Posted in Combinatorics, Conferences, personal, Probability | Tagged | 2 Comments

Jiaoyang Huang, Theo Mckenzie, Horng-Tzer Yau: Ramanujan Property and Edge Universality of Random Regular Graphs

Posted on January 12, 2025 by Gil Kalai

A central problem in combinatorics, probability theory, and analysis is to understand the spectrum of  random d-regular graphs G with vertices. The following paper marks a huge leap in our understanding of this problem.  Ramanujan Property and Edge Universality of … Continue reading →

Posted in Analysis, Combinatorics, Probability | Tagged , , , | 1 Comment

The Answer to TYI (57): In Dimension Three or More, Intuitive Norms are Euclidean

Posted on January 10, 2025 by Gil Kalai

Consider equipped with a norm. Given a finite set of points and a point , we consider , the sum of distances from to the points in . Next we consider the set of points that attain the minimum of … Continue reading →

Posted in Convexity, Geometry, Test your intuition | Tagged , , | 3 Comments

Test Your Intuition (57): Are All Norms Nice?

Posted on January 7, 2025 by Gil Kalai

Update: For the answer, see this post. Consider equipped with a norm. Given a finite set of points and a point , we consider , the sum of distances from to the points in . Next we consider the set … Continue reading →

Posted in Convexity, Geometry, Test your intuition | Tagged , , | 17 Comments